arXiv math/01071542001-07-20math.FAmath-phmath.MP

Distribution Functions for Random Variables for Ensembles of positive Hermitian Matrices

Estelle L. Basor

发表信息：: Communications in Mathematical Physics 188, 327-350
DOI：: 10.1007/s002200050167

英文摘要：

Distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive Hermitian matrices. The inverse Fourier transform of the distribution is shown to be a Fredholm determinant of a certain operator that is an analogue of a Wiener-Hopf operator. The asymptotic formula shows that up to the terms of order $o(1)$, the distributions are Gaussian.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Characterization of preorders induced by positive maps in the set of Hermitian matrices

Uhlmann showed that there exists a positive, unital and trace-preserving map transforming a Hermitian matrix $A$ into another $B$ if and only if the vector of eigenvalues of $A$ majorizes that of $B$. In this work I characterize the existence of such a transformation when one of the conditions of unitality or trace preservation is dropped. This induces two possible preorders in the set of Hermitian matrices and I argue how this can be used to construct measures quantifying the lack of positive semidefiniteness of any given Hermitian matrix with relevant monotonicity properties. It turns out th…

2021-05-18math-phmath.FAmath.MP

Positive matrices partitioned into a small number of Hermitian blocks

Positive semidefinite matrices partitioned into a small number of Hermitian blocks have a remarkable property. Such a matrix may be written in a simple way from the sum of its diagonal blocks

2012-10-10math.FA

Cayley transform and the Kronecker product of Hermitian matrices

We consider the conditions under which the Cayley transform of the Kronecker product of two Hermitian matrices can be again presented as a Kronecker product of two matrices and, if so, if it is a product of the Cayley transforms of the two Hermitian matrices. We also study the related question: given two matrices, which matrix under the Cayley transform yields the Kronecker product of their Cayley transforms.

2013-07-17math.FA

Decomposition and partial trace of positive matrices with Hermitian blocks

Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important inequalities in quantum information theory such as the Nielsen-Kempe separability criterion.

2012-10-11math.FA

On Symmetric Norm Inequalities And Hermitian Block-Matrices

The main purpose of this paper is to englobe some new and known types of Hermitian block-matrices $M=\begin{pmatrix} A \& X\\ {X^*} \& B\end{pmatrix}$ satisfying or not the inequality $\|M\|\le \|A+B\|$ for all symmetric norms

2015-11-23math.FAmath.OAmath.RA

Diagonalizing hermitian matrices of continuous functions

The problem of diagonalizing hermitian matrices of continuous fiunctions was studied by Grove and Pederson in 1984. While diagonalization is not possible in general, in the presence of differentiability conditions we are able to obtain positive results in the case of $2\times 2$ matrices. It remains open whether our results can be extended to $n\times n$ matrices.

2012-12-22math.FAmath.OA

更多相关论文收起更多论文

J-厄米特矩阵锥上的Kubo Ando均值

Kubo Ando Means on the Cone of J Hermitian Matrices

University of North Florida（北佛罗里达大学）

本文将Kubo-Ando均值理论扩展到正四元数厄米特矩阵锥，并针对J-厄米特正矩阵锥建立类似框架，证明其均值与算子单调函数一一对应，扩展了经典特征到不定情形。

2026-08-06math.FA

Positive definite matrices with Hermitian blocks and their partial traces

Let $H$ be a positive semi-definite matrix partitioned in $β\times β$ Hermitian blocks, $H=[A_{s,t}]$, $1\le s,t,\le β$. Then, for all symmetric norms, {equation*} \| H \| \le \| \sum_{s=1}^β A_{s,s} \|. {equation*} The proof uses a nice decomposition for positive matrices and unitary congruences with the generators of a Clifford algebra. A few corollaries are given, in particular the partial trace operation increases norms of separable states on a real Hilbert space, leading to a conjecture for usual complex Hilbert spaces.

2012-09-09math.FA

Supports for minimal hermitian matrices

We study certain pairs of subspaces $V$ and $W$ of $\mathbb{C}^n$ we call supports that consist of eigenspaces of the eigenvalues $\pm\|M\|$ of a minimal hermitian matrix $M$ ($\|M\|\leq \|M+D\|$ for all real diagonals $D$). For any pair of orthogonal subspaces we define a non negative invariant $δ$ called the adequacy to measure how close they are to form a support and to detect one. This function $δ$ is the minimum of another map $F$ defined in a product of spheres of hermitian matrices. We study the gradient, Hessian and critical points of $F$ in order to approximate $δ$. These results allo…

2019-06-14math.FAmath.OA

Inverses of moment Hermitian matrices

Motivated by [9] we study the existence of the inverse of infinite Hermitian moment matrices associated with measures with support on the complex plane. We relate this problem to the asymptotic behaviour of the smallest eigenvalues of finite sections and we study it from the point of view of infinite transition matrices associated to the orthogonal polynomials. For Toeplitz matrices we introduce the notion of weakly asymptotic Toeplitz matrix and we show that, under certain assumptions, the inverse of a Toeplitz moment matrix is weakly asymptotic Toeplitz. Such inverses are computed in terms o…

2013-11-14math.CAmath.FA

Hermitian和正常矩阵的特征值稳定性

Eigenvalue stability of Hermitian and normal matrices

Université Côte d’Azur（蔚蓝海岸大学）；TU Wien（维也纳工业大学）

研究Hermitian和正常矩阵特征值映射的连续性，证明其在Sobolev空间中的非均匀连续性，并探讨其在奇异值、矩阵条件数等应用中的稳定性。

2026-03-24math.APmath.CAmath.FA